will my playstation 2 be able to play region 2 encoded disks.

If it can't what dvd player should I buy that does support playing them.

If you could provide us with a bit more information we surely could help you. If you bought a japanese or european PS2 you can of course play RC2 discs. If you bought a japanese PS2 when they first hit the shelves you probably can play all regions as the DVD drivers were faulty.
Otherwise you want to look here.

I have a U.S playstation 2 will it be able to play region 2 disks?

No. Not unless you modified it to play other regions.